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Construct a bicentral trapezoid using only a ruler ;)

Source: XVII Sharygin Correspondence Round, P21

March 2, 2021
geometrytrapezoid

Problem Statement

A trapezoid ABCDABCD is bicentral. The vertex AA, the incenter II, the circumcircle ω\omega and its center OO are given and the trapezoid is erased. Restore it using only a ruler.
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